Unfortunately, Postgres is not really embed-able into an application, in the sense that h2 and sqlite are embedded databases. Postgres is designed to be used in a client-server fashion, and will have to run in the background as a separate process. If you really need to use postgres, I suppose you could include an initdb into your application installation process, such that when you start/run your application, it can spawn a Postgres process, do the work needed, then shut it down when you quit the application. However, I think you may run into some performance issues, since you'll need to spend time waiting for Postgres to start up/shut down.
I'm curious, however--what are the features in your application that make Postgres a requirement?
HTH,
--Richard
